Measurements of Isomeric Yield Ratios of Proton-Induced Fission of U and Th

Vasileios Rakopoulos Measurements of Isomeric Yield Ratios of Proton-Induced Fission of natU and natTh

at the IGISOL-JYFLTRAP facility

Abstract This thesis presents the measurements of isomeric yield ratios of fission products in 25 MeV proton-induced fission of nat U and nat Th, performed at the Ion Guide Isotope Separator On-Line (IGISOL) facility at the University of Jyväskylä. Knowledge of the relative intensities of metastable states produced in fission is of importance for various fields of nuclear physics, both fundamental and applied. The angular momentum of fission fragments is regarded as an important quantity in order to understand the fission mechanism because it can provide information on the scission configuration. One of the means to deduce the angular momentum of highly excited nuclei is by determining the yield ratio of low lying isomeric states. Isomeric yield ratios are also important themselves for simulations of processes such as the r-process, which is believed to be terminated by the fission of very neutron-rich heavy nuclei, and the neutronics and decay heat of nuclear reactors. In addition, proper simulation of the effect of delayed neutrons in a reactor requires accurate knowledge of the population of isomeric states, since the β-delayed neutron emission probability from the isomeric state can be an order of magnitude different from that of the ground state. The measurements were performed from 2010 to 2014, both at IGISOL-3 and at the recently upgraded and relocated IGISOL-4 facility. With the IGISOL method short-lived fission product yields can be measured and, by employing the high resolving power of the Penning trap JYFLTRAP, isomeric states separated by a few hundred keV from the ground state can be observed. Thus, a direct determination of the isomeric yield ratios by means of ion counting, registering the products in less than a second after their production has been accomplished for the first time. In addition, γ-spectroscopy was employed in order to verify the consistency of the experimental method. Isomeric yield ratios of fission products were measured in a wide mass range (A = 81 to 130) for 25 MeV protons on nat U and nat Th. Specifically, six isomeric pairs (81Ge, 96Y, 97Y, 97Nb, 128Sn and 130Sn) with suitable half-lives were measured and indications of a dependence of the production rate on the fissioning system were observed. A 25 MeV proton beam was selected as there are experimental data available in the literature, determined by means of γ-ray spectroscopy, so that a comparison of the results could be performed.

"survive another winter" to Katerina and Elias-Sebastian

List of papers

List of papers is not included in this thesis.

Contents

Preface ...... 1

1 Introduction ...... 3 1.1 A (brief) introduction to ﬁssion ...... 3 1.2 Isomers ...... 9 1.3 The importance of isomeric yields ...... 10 1.4 Fission yields measurements techniques ...... 13

2 Experimental Facility ...... 17 2.1 The IGISOL technique combined with JYFLTRAP ...... 17 2.2 Description of experimental elements ...... 18 2.2.1 The ﬁssion ion guide ...... 18 2.2.2 Mass separator ...... 21 2.2.3 Radio-Frequency cooler and buncher ...... 21 2.2.4 Isobaric puriﬁcation with JYFLTRAP ...... 22 2.2.5 Timing Structure of the measurement ...... 25 2.3 Chemical effects of IGISOL and JYFLTRAP ...... 26

3 Data Analysis ...... 29 3.1 Penning Trap Data ...... 29 3.1.1 Time of flight selection ...... 30 3.1.2 Peak intensity determination ...... 31 3.1.3 Corrections due to radioactivity ...... 34 3.2 γ-spectroscopy Data ...... 36 3.2.1 Efficiency calibration ...... 37 3.2.2 Decay corrections ...... 39 3.2.3 Transport efficiency ...... 42 3.2.4 Uncertainties ...... 42

4 Results and Discussion ...... 43 4.1 Presentation of the results ...... 43 4.2 Discussion and comparison ...... 44 4.2.1 Mass 81 ...... 46 4.2.2 Mass 96 ...... 48 4.2.3 Mass 97 ...... 48 4.2.4 Mass 128 ...... 49 4.2.5 Mass 130 ...... 50 4.3 General remarks ...... 50 5 Summary and Conclusions ...... 53 5.1 Summary ...... 53 5.2 Conclusions ...... 53

References ...... 56 List of Figures

Fig. 1.1: Nucleus deformation in terms of a liquid drop model ...... 4 Fig. 1.2: Potential energy surface of deforming nucleus ...... 6 Fig. 1.3: Double-humped fission barrier ...... 7 Fig. 1.4: Time scale of fission fragments de-excitation ...... 9 Fig. 1.5: Decay paths of nuclides ...... 10 Fig. 1.6: De-excitation of the fission fragments ...... 11 Fig. 1.7: Decay scheme of mass chain A=115 ...... 12 Fig. 2.1: IGISOL and JYFLTRAP facility ...... 19 Fig. 2.2: The fission ion guide at IGISOL ...... 20 Fig. 2.3: Ion’s trajectory in the Penning Trap ...... 23 Fig. 2.4: Conversion of the ion’s motion in the trap ...... 24 Fig. 2.5: Timing structure of the measurement ...... 26 Fig. 3.1: Time of flight distribution of mass A=96 ...... 30 Fig. 3.2: Mass spectrum without and with TOF gating ...... 31 Fig. 3.3: Frequency distribution of mass A=96 ...... 33 Fig. 3.4: γ-ray spectrum of mass A=128 ...... 38 Fig. 3.5: HPGe intrinsic efficiency curve ...... 39 Fig. 4.1: Isomeric yield ratios ...... 45 Fig. 4.2: Frequency spectrum for mass A=81 ...... 47 Fig. 4.3: γ-ray spectrum for mass A=81 ...... 47 Fig. 4.4: The case of multiple results ...... 49 Fig. 4.5: Investigation of the IYR dependence on the fissioning system ... 51 Fig. 4.6: IYR as a function of the spin difference of the states ...... 52

Preface

This thesis reports on the experimentally deduced isomeric yield ratios from proton-induced fission on natU and natTh. All the measurements were performed at the IGISOL-JYFLTRAP facility at the University of Jyväskylä over a span of four years, from April 2010 to May 2014. This work was accomplished as part of the collaboration between Uppsala University and the University of Jyväskylä that aims at high precision measurements of fission yields. Since the fission yields are an important characteristic of the fission process, a brief introduction of the latter is attempted in Chap- ter 1, where a description of the time evolution of the fission and a definition of the fission yields are given. In addition, the importance of the knowledge of the population of the isomeric states for both fundamental and applied physics is emphasised, as motivation for the present work. At the end of the chapter different techniques of measuring fission yields are described. During this period of four years, a lot have changed at the IGISOL facility since a major upgrade was realised, both in the IGISOL and JYFLTRAP fa- cilities. Chapter 2 gives an overview of the renewed facility, highlighting the most important elements along the beam line. In Chapter 3, the analysis procedure which was developed and followed in order to deduce the yield ratios of the acquired data is presented. The results of this analysis are presented in Chapter 4, together with some remarks that could be drawn as an outcome from the comparison of the results with each other and with experimental data available in the literature. Last, in Chapter 4 the conclusions of this study are summarised, and some plans for the future are mentioned as well. I was involved in one of the performed experiment, in April 2014. My contribution to this sequence of measurements was to develop the analysis routine, deduce the isomeric yield ratios and compare the obtained results.

1. Introduction

1.1 A (brief) introduction to fission Fission was first observed experimentally in January 1939 by Otto Hahn and Fritz Strassmann [1]. The reaction in which fission was studied was neutron- induced fission of Uranium. In the process a heavy nucleus decays into two fragments of comparable mass. It was first discussed quantitatively by Lise Meitner and Otto Frisch [2], who discussed the process in terms of a liquid drop, which becomes deformed and which beyond a critical deformation is breaking apart into two pieces, the fission fragments. The same year, N. Bohr and J. A. Wheeler in their prominent work gave an extended theoretical description of fission [3]. The mechanism of fission is a very complicated process and we are still far from a detailed understanding. That’s why although fission induced by neutrons in the actinides is perhaps the most studied reaction of nuclear physics, a complete picture of the process is still lacking. From the perspective of the liquid drop model (LDM) description, a neutron that enters into the actinide target adds excitation energy to the compound nucleus, resulting in shape deformations and change in the potential energy, which increases above the level of the ground state. In the landscape of deformation, there is a critical deformation of no return, which is called the saddle point, as can be seen in Fig. 1.1. Afterwards, with further deformation, a situation is reached where the neck joining the two nascent fragments is no longer stable but is breaking apart. The snapping of the neck is called scission. Thereafter, the fragments1 are created in general with unequal masses. The available energy in fission is approximately 200 MeV and is shared between the total kinetic energy (TKE) and total excitation energy (TXE) of the fragments. In order to de-excite, the fragments will emit neutrons (secondary prompt neutrons) and the process is completed with γ-rays emission. The binding energy (B) of a nucleus can be described by the semi-empirical formula of Bethe-Weizsäcker, based on the liquid drop model (LDM) [4]: 2/3 −1/3 2 −1 B = αν A − αsA − αcZ(Z − 1)A − αsym(A − 2Z) A + δ (1.1) • the first term stands for the volume term, which increases with increasing number of nucleons. It is referred to as the volume energy (Eν ) and it is the most important factor of the formula, especially for the lighter nuclei.

1The formation of two fragments (binary fission) is much more likely than the formation of three (ternary fission), which occurs with a low probability of only a few events per 1000 fissions.

3 n

Saddle

Scission

secondary Fragment II Fragment I neutrons

Fig. 1.1. Visualisation of the nucleus deformation in terms of a liquid drop.

• the second term gives the surface energy (Es), which describes the fact that nucleons on the surface have less neighbours to interact with, resulting in a decrease in the binding energy. • the third term, the Coulomb term (Ec), expresses the repulsive interactions between the protons in the nucleus due to the Coulomb force, and it contributes to the split of the nucleus. In cases, like fission, where the nucleus deforms considerably, this might become an important term because the Coulomb repulsion might overcome the short range of the strong nuclear force. • the fourth term, which is called the symmetry energy (Esym), describes the tendency of the nucleus to become symmetric in protons and neutrons in order to be stable. This term is more important for light nuclei, since for the heavier ones the increase in Coulomb repulsion requires additional neutrons for nuclear stability. • the last term, which is called the pairing term (Ep), expresses the tendency of nucleons to couple pairwise in order to form stable configura- tions. Specifically this term does not contribute when A = odd (odd Z and even N and vice versa), δ = 0. However the relatively high stability of even-even nuclei is taken into account by a positive contribution (+δ) to the total binding energy EB of the nucleus, and the relatively low stability of odd-odd nuclei by a negative contribution (−δ).

4 The surface and the Coulomb energy terms in Eq. 1.1 are the only ones which are affected when a liquid drop becomes deformed. Speciﬁcally, the surface energy term is smaller for a sphere, but any deformation away from this shape is associated with larger potential energy from this effect. The Coulomb energy term is decreased with a deformed nucleus, because of the larger average separation between the charge elements. A radius vector R(θ) of the nucleus can describe the small axially symmetric deformation:

R(θ) = R0[1 + α2 P2 cos(θ)] (1.2) where θ is the angle of the radius vector, α2 is a coefﬁcient that describes the amount of the deformation, R0 is the radius of the non deformed nucleus and P2 is the second order Legendre polynomial [5]. The surface (Es) and the Coulomb (Ec) energies for small deformations, were calculated by Bohr and Wheeler: 2 1 E = E0(1 + a2) and E = E0(1 − a2) (1.3) s s 5 2 c c 5 2

0 0 where Es and Ec are the surface and Coulomb energies respectively without any deformation. In order for a spherical nucleus to be stable against deforma- 1 2 0 tion the decrease in Coulomb energy ∆Ec=- 5 α2 Ec must be smaller than the 2 2 0 increase in the surface energy ∆Es= 5 α2 Es . The drop will become unstable when the absolute values of the aforementioned terms equal each other, when 0 0 Ec=2Es . Thus, as introduced by Bohr and Wheeler, the notion of the fissility x can be defined: 0 Ec x = 0 (1.4) 2Es For x less than unity the nuclei are stable, while for x bigger than unity there will be no potential energy barrier to inhibit spontaneous fission of the drop. In order to describe the large deformations that are encountered on the top of the fission barrier, higher order polynomials must be included in Eq. 1.2:

R(θ) = (R0/λ)[1 + ∑ αn Pn cos(θ)] (1.5) n=1 where the parameter λ ensures that the volume remains constant. The potential energy of the deformation is increasing as expected for small deformation, as can be seen in Fig. 1.2. There is though, a crucial point which is reached for specific values of the deformation parameters. This point is called saddle, and a fissioning nucleus moving along the path of deformation has to overcome the potential barrier at this point, the fission barrier B f . The height of this fission barrier for the actinides is about 6 MeV above the ground state. Beyond this, a path of minimum energy slopes downwards until the nucleus is breaking apart at scission [6].

5 E*

En saddle point

Sn Energy

scission point

Deformation

Fig. 1.2. The potential energy as a function of the deformation of a nucleus. The ﬁssion barrier (B f ), as classically approached by the LDM model with a single humped barrier, is also noted. On the left side the neutron separation energy (Sn) and the additional excitation energy, added to the compound nucleus from the extra neutron, appear as well. On the top of the ﬁgure, the deformation of the nucleus from spherical shape to scission point is illustrated.

The addition of a neutron to the target nucleus contributes to the binding energy of the formed compound nucleus, so that the latter might excite above the fission barrier, as illustrated in Fig. 1.2. The amount of excitation energy which needs to be added to the system in order to overcome the fission barrier is strongly case dependent. Nuclei with even mass number A, such as 238U, exhibit a higher fission barrier than the energy required to separate a neutron (neutron separation energy), Sn, so more energy from the incident particle is required in order to fission. This happens because the extra neutron will not be paired to the nucleus, as all nucleons are already in pairs, so extra energy is needed for the compound nucleus 239U to undergo fission. For 238U, the neutron separation energy and the fission barrier of the formed compound nu- 239 ∗ cleus U are Sn = 4.8 MeV and B f = 6.3 MeV respectively. On the other hand, nuclei with odd mass, such as 235U which is very well studied for its use in nuclear reactors, exhibit a neutron separation energy higher than their fission barrier. That means that the extra neutron will readily pair with another nucleon, so that the excitation energy will increase above the fission barrier.

6 For 235U, the neutron separation energy and the fission barrier of the formed 236 ∗ compound nucleus U are Sn = 6.5 MeV and B f = 5.6 MeV respectively. The simple liquid drop model, although it describes the general properties of the fission process relatively well, has certain limitations when it is called to explain experimental results. For example, it fails to explain the two dis- tinct modes of symmetric and asymmetric mass division in fission, which was suggested from experiments. Maria G. Mayer, in her work in 1948, traced the asymmetric fission back to nuclear shell effects, in particular to the stabilising influence of the 50 proton shell and the 82 neutron shell that coincide in the spherical doubly magic 132Sn [7]. Moreover, it’s not possible to predict the isomeric fission with the single fission barrier of the LDM description. Shell effects "corrections" were introduced to the liquid drop model by Strutisky [8], thus all the processes that could not be explained by the single-humped model could be attributed to shell effects.

Energy

Mass Distribution

Normal Fission

EA EB

Isomeric Fission II

Spontaneous Fission I

εI εII Deformation

Fig. 1.3. Illustration of the double-humped ﬁssion barrier as introduced by shell corrections. Humps at A and B result in minima in potential energy at deformation of εI and εII. States in these wells are designated class I and class II, respectively.

In Fig. 1.3, the "shell-corrected" description of the fission process is visualised, where it can be noticed that the fission barrier becomes double-humped, instead of single. On the top of the same figure the different stages of the shape deformation of the nucleus along the fission path are visualised. As can be seen, the shape of the compound nucleus is already deformed in the ground

7 state, which lies in the first minimum and it is designated as εI in Fig. 1.3. The second minimum, designated as εII, can explain the isomeric fission. The shape of the nucleus in this second barrier well is elongated due to repulsion of the number of protons. It has a higher energy than the ground state, so it is metastable. In this case, the isomerism is observed due to the difference in the shape of the nucleus, and not to be confused with the spin isomers, produced due to the differences in the spins of the states, and measured in the present work. The nucleus is trapped into retaining its elongated shape since its energy is not sufficient to surmount either barrier. Although the decay of the nucleus is not possible with the classical approach, since its energy is below the fission barrier, it still may occur by tunnelling through the barrier according to quan- tum mechanics. Actually, this can happen both ways. It can tunnel back to its more spherical ground state by emitting a γ-ray, as an ordinary nuclear isomer, leaving its identity isotopically unchanged. It can also tunnel to the other direction, by producing two separate fragments by fission. Spontaneous fission may occur when the nucleus is on the ground state and tunnel through the whole fission barrier, without needing any additional excitation energy from a particle. Between the two barrier wells, discrete excited states exist (referred to as class-I and class-II), which become less resolved the higher excitation reached, until as always they enter the continuum level densities region, where they are unable to be resolved. The excited states on the saddle points are referred to as "transition states" and they have their characteristic spin and parity.

Time scale of the de-excitation of the fission process A mention explicitly must be done here on the distinction between fission fragments and products, since this is closely related to the time evolution of the fission process itself. The fission fragments are highly excited so, in order to cool down they emit neutrons and γ-rays. The time scale involved in the fission process is shown in Fig. 1.4. The evaporation times for neutrons are much shorter than the emission time of γ-rays, so they first de-excite by neutron emission. After prompt neutron emission the "primary" fragments are called "secondary" or just "products" and their remaining excitation energy is below the neutron separation energy. The only way for the nucleus to de-excite more thus, is by emitting γ-rays. The transition from neutron to gamma emission happens on a time scale of 10−14 s, while the emission of prompt γ-rays may last for several ms. After this de-excitation process, fission products reach their ground states, but they are still too neutron-rich and hence unstable and liable to β −-decay. This decay may last from several ms up to years. The radioactivity of fission products is part of the activity of fuel remnants from nuclear power stations. It is worth mentioning that once the saddle has been passed the fission process is very fast, while it takes comparatively long time to evaporate a neutron.

8 Fission Fragments Fission Products

Primary Fragments Secondary Fragments

-21 -20 -3 t Time scale (s): 10 10 10-18 10-14 10

saddle to prompt neutrons prompt γ-rays β-decay: β-particles, delayed scission neutrons, γ-rays and ﬁssion

Light charge particles Scission neutrons Fig. 1.4. Time scale in the de-excitation of ﬁssion fragment

Definition of fission yields Measurements of the fission observables such as the mass yield distributions of the fission products can provide important information about the fission process itself, either for fundamental or applied physics. In Fig. 1.5 part of the chart of nuclides is illustrated, where the possible decay paths of each nuclide can be seen. The β −-decay is denoted with the black arrows and the neutron emission with the red arrows. Based on this figure and the time scale presented in the previous paragraph the fission products are categorised as follows [9]: 1. Independent fission yields: a measure of the number of atoms of a specific nuclide produced directly in the fission process before any radioactive decay. 2. Cumulative fission yields: describes the total number of atoms of a specific nuclide produced directly in fission and after the decay of all of its precursors. 3. Total chain yields: expresses the cumulative yield of the last, either stable or long-lived member of an isobaric chain. 4. Mass number yields: is the sum of all independent yields of a particular isobaric chain. The difference between the total chain yield and the mass number yield emerges from the contribution of β-delayed neutrons. The former contains the produced nuclides after the β-delayed neutrons, while the latter does not. If there is no emission of delayed neutrons, the two yields concur.

1.2 Isomers In Fig. 1.6 the de-excitation process of the fission fragments is illustrated. The fragments produced in fission can be characterised by their distribution of excitation energy and initial angular momentum. As explained earlier, the highly excited fragments first de-excite by emitting prompt neutrons and then prompt γ-rays. As long as the excitation of the fragments is high the neutron emission prevails, until the excitation energy is reduced below the neutron emission threshold. Afterwards, the emission of γ-rays prevails, at the beginning with statistical E1 emission. The change in the angular momentum due to the emis-

9 130Te 131Te 132Te

β-

129Sb 130Sb 131Sb 132Sb n

Proton Number Z Number Proton 128Sn 129Sn 130Sn 131Sn 132Sn

128In 129In 130In 131In 132In

128Cd 129Cd 130Cd 131Cd 132Cd

N eutron Number N

Fig. 1.5. In ﬁgure the decay paths of part of the chart of nuclides is illustrated. The black arrows represent β-decay and the red arrows represent the delayed neutron emission.

sion of the prompt neutrons and the statistical γ-rays is small. In the region close to the yrast line, non-statistical (mostly E2) photons carry away the remaining angular momentum. Most of the isomeric states are formed in this region. Isomeric states are metastable states that occur when the angular momentum difference between two states is large. Under these circumstances, the electromagnetic transition probabilities from these states are reduced, because of their high multipole order, resulting in an unusually long lifetime, compared to other excited states. In the shell model picture, these states are formed because major shells are occupied by particles of high angular momentum, while their close in energy sub-shells are occupied by particles of low-angular momentum. Speciﬁcally the major shell closures occur at Z, N = 50, 82 and 126 particles on the levels 1g9/2, 1h11/2, and 1i13/2 respectively, while the adjacent lower sub-shells are occupied by 2p1/2, 2d3/2 and 3p1/2 [10].

1.3 The importance of isomeric yields Isomeric states encompass a wide range of lifetimes due to several reasons: their state transitions occur in various multipole type and order (E3, M3, E4, M4, ...), while their decay modes compete between internal conversion and

10 Primary * E Fission Fragments E*

n n

Secondary E (Yrast) Fission Fragments

γ γ Statistical γ

Sn Discrete levels γ γ } γ J

Fig. 1.6. Illustration of the de-excitation of the ﬁssion fragments ﬁrst by prompt neutrons emission and then by statistical (E1) γ-rays. Afterwards, the emission of non-statistical photons takes place to the region close to the yrast line.

β-decay. Similarly, the ground states to which the metastable states will decay, unless a β-decay occur either from these states or from an intermediate lower lying level along their decay path, exhibit a similar span of lifetimes, from milliseconds to stability. Thereafter, it becomes evident that a description of the time evolution of the excited states must take into account this variation in half-lives where the population of the isomeric states cannot be ignored. In Fig. 1.7 an example of the decay path of mass A=115 is given in order to visualise how the presence of the metastable states can complicate the decay path and branching ratios of an isobaric chain. As can be noticed, 115Rh decays by β-particle emission to 115Pd. In 115Pd, the isomeric state at 89.2 keV can decay either by the dominant in this case β-particle emission (probability of 92%) to 115Ag or to the ground state by internal conversion with a smallest probability of 8%. In addition, the isomeric state in 115Ag complicates further the situation since its de-excitation competes between β-decay (79%) and internal conversion to the ground state (21%). As mentioned in the previous section, the ﬁssion products are either stable or unstable to β-decay and/or to delayed neutron emission. Unstable products can decay to either nuclides where no isomeric states exist, or to species occupying their (stable or not) ground state or their metastable isomeric state. The time development of the energy release in the latter case depends crucially on the initial relative populations (branching fractions) between isomeric and ground states. For example, in the case of thermal-neutron ﬁssion of actinide nuclei, such as 233,235U or 239,241Pu, roughly 800 primary products are formed. Approximately 700 of these products are unstable and about 150 have known

11 0.99 s 7/2+ 0 keV 115Rh β- : 100%

50 s 11/2- 89.2 keV

IT: 8% β- : 92% 25 s 5/2+ 0 keV 115Pd β- : 100%

18.0 s 7/2+ 41.2 keV

IT: 21% β- : 79% 20.0 m 1/2- 0 keV 115Ag

β- : 100%

Fig. 1.7. Decay scheme of part of the mass chain A=115. The complications that arise in the decay path due to the different decay modes of the metastable states can be seen. The ground states are illustrated with the thick lines, while the isomeric states with the thinner ones.

isomeric states with half-lives τ ≥ 0.1 s [11]. The importance of isomeric states in calculations of fission products decay energy release, such as the decay heat calculations, is thus clear. In addition, the β-delayed neutron emission probability from the isomeric state can be up to an order of magnitude different from that of the ground state (e.g. 0.33% for 98Y, 3.5% 98mY according to NuDat2 [12]). Therefore, a proper simulation of the effect of delayed neutrons in the nuclear reactors requires accurate knowledge of the population of isomeric states in fission. Moreover, the knowledge of the population of the isomeric states is important in yield measurements of fission products. In such studies, close-lying isomeric states to the ground state of a nuclide might create peak multiplets that are difficult to resolve. Thus, the yields of isomeric and ground states are often summed together. In order to apply corrections for the population of the metastables states knowledge of their intensity relative to the ground state intensity is needed. It is worth mentioning that the shorter the isomer’s half-life is compared to the ground state’s lifetime, the more significant the correction is. So far the importance of isomeric states to applications has been described. Nevertheless the isomeric yield ratios are important for simulation of processes such as the astrophysical r-process. The r-process is believed to be

12 terminated by the fission of very neutron rich heavy nuclei, while the fission fragments return to the r-process path. Furthermore, the neutron capture of the high spin isomeric state can be very different compared to the one of the low spin ground state. Hence, these simulations need as accurate knowledge as possible of the population of isomeric states. The fissioning systems that ter- minate the r-process are more neutron rich than any of those that can currently be reached in the experimental frame, so their yields are estimated based on theoretical calculations. In order to test the ability of the theories to reproduce the isomeric yield ratios of the fissioning system, they have to be determined experimentally. Besides all the aforementioned reasons for which isomeric yields are important themselves, they can also be used in fundamental physics, in the effort for a better understanding of the fission process. The angular momentum of the fission fragments can provide better information on the scission configuration. One of the possible means to deduce the angular momentum of the fragments is the independent isomeric yield ratio of fission products, which can be used to study the collective rotational degrees of the fissioning system at the scission configuration. In [13], and the references therein, more information can be found on the deduction of the root mean square angular momentum of the primary fragment (Jrms), while in [14] information on the deduction of the properties of scission configuration can be found. In the first efforts to deduce the Jrms, time consuming radiochemical separation techniques were used, resulting in limitation on the isomeric pairs, because these had to be located close to the valley of stability and shielded by stable or long-lived isotopes from production via the beta decay of more neutron-rich isotopes. In more recent works, [15][16], direct γ-ray counting was employed and the deduced production via β-decay is simply subtracted from the total yield.

1.4 Fission yields measurements techniques The measurement of fission yields is a complicated process because the fission fragments are not formed in a single way. Therefore several different techniques have been developed over the years aiming at measuring the cumulative or the independent yield, each one with its own advantages and draw- backs. They can mainly be distinguished in two main categories: • measurements of stopped fragments. • measurements of unstopped fragments. The oldest technique in the first category is radiochemical separation of the longest lived isotopes of fission products. Then, the activity could be determined via β- or γ-spectroscopy. At the beginning, the method was time consuming, so it was able to measure only long-lived isotopes. After some development, short-lived isotopes with a life-time of the order of seconds or less could be identified as well, and even isomers in some cases.

13 Fission products can also be measured by means of mass spectroscopy, making use of radioactive beams. Specifically with the Isotope Separator On-Line (ISOL) technique, a thick target is irradiated, and the created products are introduced to an ion source, where they are ionised. Afterwards the ions are mass separated by means of magnetic separation, resulting in pure ions beams, which can be detected by ion counters. The fission products can also be detected by means of γ-spectroscopy, since the β-decay of the products is followed by γ-ray emission. If products are adequately long-lived so that their decay occurs after the mass separation, the unique γ-ray spectrum of each isobaric chain can be employed. The drawback of this method is that it is slow since a thick target is used in order to create a sufficient yield of a product. Moreover the universal use of this method is hindered by the limitations that arise from the use of the ion source. Although in fission a large variety of nuclides is produced, there is not an ion source that can be used for all of them since the chemical selectivity of the ion source is governed from the different ionisation properties of the elements. In order to measure independent fission yields a variant of this technique has been developed. Specifically with the Ion Guide Isotope Separation On- Line (IGISOL) technique, a thin target is connected directly in the ion source so that the method is fast and ions of all chemical elements can be produced. However, one of the biggest issues of this method is its limited mass resolving power, resulting in longer irradiation time in order to overcome this problem. In addition the decay scheme of the most exotic nuclei is not well known in some cases. Direct measurement of γ-rays can be performed as well in case of very exotic targets, since with this method a very small amount of the sample is required. On the other hand, the data analysis is complicated and accurate knowledge of the decay scheme is necessary. Moreover in the case of independent yield measurement, the decrease in the irradiation time, results in reduced statistics and consequently in larger uncertainties. The methods described above regard measurements of stopped fission products. Measurements of fission products without stopping them can be achieved as well. In these techniques, by measuring the kinetic energy and velocity of one fission fragment, the (E,υ) method, or of both fission fragments, the (2E,2υ) method, and based on the conservation of momentum in fission, the masses of the fission fragments are calculated. A low-energy and light particle- induced fission is one of the requirements of the method, so that the momentum of the inducing particle can be ignored. Another requirement is a thin target, in order to minimise as much as possible the energy loss of the fission fragments in the target. For the velocity measurement the time of flight technique is applied, while for the energy measurement surface barrier detectors may be used. Recoil spectrometers, such as Lohengrin at the Institut Laue-Langevin (ILL) in Grenoble [17], use the (E,υ) technique for studying unstopped fission frag-

14 ments. These spectrometers are coupled to the intense neutron flux of a reactor, and they achieve a mass separation by electromagnetic separation based on the energy-charge state ratio (E/q). Specifically the spectrometer at ILL, performs an additional separation based on the mass-charge state ratio (A/q). Therefore, one of the disadvantages of this method is that in order for an independent yield distribution to be observed, the measurements have to be repeated for several kinetic energies and charge states. Spectrometers, such as the Cosi-fan-tutte spectrometer at ILL, that make use on the (2E,2υ) technique, by measuring the time of flight and energy of each fission product, also exist, in this way avoiding the need of electro- magnets. More spectrometers have been constructed recently, like VERDI (VElocity foR Direct particle Identification) [18] constructed for the Joint Re- search Centre IRMM, Geel, Belgium, or are planned to be installed in the near future, like the FALSTAFF (Four Arm cLover for the STudy of Actinide Fis- sion Fragments) spectrometer [19], to be installed in the Neutrons for Science (NFS) facility in SPIRAL2 [20], or the SPIDER spectrometer (SPectrometer for Ion DEtermination in fission Research), located at the Los Alamos Na- tional Laboratory [21]. For identifying the nuclear charge the (∆E,E) technique is employed. The energy loss (dE/dx) of an ion passing through a material of known thickness, due to interactions of the ions with the shell electrons of the matter, depends on the kinetic energy and charge Z of the ion. By measuring the energy loss ∆E and the kinetic energy E, the nuclear charge Z of the nuclides can be deduced. Another method for measuring fission yields, relatively recent, is based on the inverse kinematics. The nuclide of interest is used as a projectile, accelerated to relativistic energies, and impinging on a stationary target. Because of its interaction with the target, the projectile excites, resulting in fission. The fission fragments are then separated in fragment separation, as in the case of the FRS (FRagment Separator) at GSI [22]. Studies of fission of almost any nuclide in the region above lead is possible with this method, which is one of its strongest advantages. The list of the different experimental techniques described in this section is far from complete. New techniques with improved instruments are added to the list all the time, aiming to a better understanding of the fission proocess.

The IGISOL technique A new method in order to improve the fission yield measurements in terms of speed and simplicity, has been developed at the University of Jyväskylä. This method couples the chemical non-selectivity of the ion guide, in the sense that ions of all chemical elements can be produced, with the superior mass resolving power of the Penning Trap located at the University of Jyväskylä (JYFLTRAP), which allows identification of ions based only on their mass. Thus it is possible to measure isotopic yield distributions for a wide range of fission products, based simply on their masses and by means of ion counting,

15 a clear distinction from the aforementioned techniques. It is worth mentioning that a high precision in the nuclide mass determination is not considered necessary, since these are used only for identification in the mass spectra. The method cannot be used merely for deducing independent fission yields distributions because of the chemical reactions introduced by the ion guide and the JYFLTRAP facility. However, if one independent yield of the isotopic yield distribution is known, the isotopic distribution can be directly converted to the fission cross-sections for the other members of the isotopic chain. This is happening because the rate of production of a particular ion in the secondary beam is directly proportional to its production cross section, since there is no significant accumulation and re-ionisation of the decay products, unlikely to the classical ion sources [23], [24]. One of the advantages of this technique is that even nuclides with very low yields can be detected thanks to the very low background. Hence, measurements of fission products can be performed, at the regions of the higher uncertainties, such as the tails or the valleys in the fission yield distribution of n-induced fission on 235U[25]. On the other hand determination of more than one fission observables is not possible with this technique, since the production of the fission fragments is integrated over several milliseconds before the yield is registered, and not on an event-by-event basis [26]. The experimental setup and procedure is described in detail in chapter 2.

16 2. Experimental Facility

2.1 The IGISOL technique combined with JYFLTRAP In June 2010, the Ion Guide Isotope Separator On-Line (IGISOL) facility at the Accelerator Laboratory of the University of Jyväskylä closed down for a major upgrade, in order to be re-commissioned as IGISOL-4 in a new experimental hall. A new 30 MeV cyclotron (MCC30/15) was housed, which has the possibility to accelerate protons (18 - 30 MeV) and deuterons (9 - 15 MeV), and is equipped with two beam lines thus offering access to a possible extraction of two beams simultaneously. The maximum intensities that have been measured inside the cyclotron are for protons 200 µA and 140 µA for 18 and 30 MeV respectively, and for deuterons 62 µA for 15 MeV, exceeding design specifications. However, it still has to be demonstrated what can be delivered and indeed handled on target [27]. IGISOL has a long tradition of experiments on both neutron-rich fission products and neutron-deficient nuclei, produced in light and heavy ion fu- sion reactions. Measurements of ground state properties, such as charge radii and masses, and decay spectroscopy were covered in these experiments [28]. In Fig. 2.1, a schematic overview of the facility is presented. The elements of the facility that are described in the text are denoted with numbers. In the case of fission related experiments, the charged particle accelerated beam (protons or deuterons), denoted with the red arrow in Fig. 2.1, impinges on a fissile target which is placed inside the fission chamber in order for the fission reaction to occur. Neutron-induced fission is planned to be realised as well, where the accelerated beam will bombard a Be target, placed in the reaction chamber, in order to produce the neutron flux which will induce fission [29],[26]. The thin target (14 mg/cm2 and 15 mg/cm2 for natTh and natU respectively) is one of the key features of the IGISOL technique, as a significant fraction of the products have enough recoil energy to pass the target and not stop within it. Helium gas is flowing into the ion guide in order to slow down the fission products. In addition due to the high ionisation potential of the buffer gas the charge of the highly charged ions is reduced to the most probable +1 state. The He gas flow and the ion guide are denoted with the green arrow and 1 in Fig. 2.1 respectively. Afterwards, the ions are transported out of the ion guide with the help of the gas flow, and then accelerated with a voltage of 30 kV and guided to the mass separator through a radio-frequency SextuPole Ion Guide (SPIG), indi- cated with 2 in Fig. 2.1, and electrostatic elements. The motivation for using

17 a multipole ion guide was to reduce the energy spread, and a higher order multipole than the common quadrupole is preferred as it can deliver higher current beam before becoming unstable (of the order of 1012 ions·s−1). More information about the SPIG can be found in [30] and the references therein. The differential pumping system is another key feature of the technique, as it allows efficient removal of the high gas load from the target chamber, while at the same time keeping a sufficiently high vacuum along the beam line. In the dipole magnet, denoted with 3 in Fig. 2.1, the first mass selection of the produced fragments takes place based on their charge to mass ratio (q/m). The mass resolving power of the magnet is m/∆m ≈ 500. The desired beam is selected by slits located at the focal plane of the dipole and through the electrostatic elements in the beam switchyard it is transferred either to the β- γ spectroscopy station or to the RadioFreQuency (RFQ) cooler and buncher, denoted with 7 and 4 in Fig. 2.1 respectively. From the RFQ cooler and buncher, the isobarically purified beam can be distributed either to the Penning Trap or the laser spectroscopy set up. In the RFQ, the preparation of the beam which will eventually enter into the Penning Trap starts. The continuous ion beam is accumulated over a period of time of several ms, and cooled with the help of helium buffer gas. The cooled ions will enter the Penning Trap in bunches with an energy spread reduced to a few eV so that a better precision can be realised in the measurement. In Fig. 2.1, the Penning Trap is denoted with 5 , while the laser spectroscopy beam line is not shown since it was not used in the present work. Inside the traps, a sequence of dipole and quadrupole excitations, as will be explained in the next section, achieve a selection of the nuclides based on their charge over mass ratio (q/m) with a resolving power up to ∼8·105, which is enough to resolve the elements of an isobaric chain, and sometimes even isomeric states. After the extraction from the Penning Trap, the ions are counted by a MultiChannel Plate (MCP) detector which is located at the end of the beam line, denoted with 6 in Fig. 2.1

2.2 Description of experimental elements In this section, the most important components along the beam line are presented. More information can be found in a series of studies related to the IGISOL and JYFLTRAP facility ( [31], [32], [33], [34]).

2.2.1 The fission ion guide One of the most important elements of the IGISOL method is the fission ion guide and the thin target which is placed within, as has been mentioned earlier. In Fig. 2.2 a schematic view of the fission ion guide, as seen from the top, is presented. The cyclotron beam, olive green arrow in the figure, irradiates the

18 Fig. 2.1. Schematic overview of the IGISOL and JYFLTRAP facility, adapted from [26].

tilted fissile target, depicted in red colour. The thickness of the target is a crucial parameter for fission yield measurements, since a too thick target hinders the products of escaping the target, while a too thin one allows the products to leave the target with too high energy, thus decreasing the probability of the fragments to be stopped by the buffer gas. By placing the target in a tilted position, it is possible to use a thin target, while its effective thickness is increased by a factor of almost ten. One of the key features of the method is the He buffer gas, which flows into the fission guide, aiming to slow down the products and cooling the target at the same time. The energy of the highly charged fission products is decreased due to a sequence of collisions with the buffer gas atoms, while their charge states are reduced via charge exchange reactions. Because of the high ionisation potential of the buffer gas a considerable fraction of the ions end up at a +1 charge state. The fission products enter the stopping chamber, which is separated from the small target volume by a thin Ni foil (0.9 mg/cm2) in order to prevent plasma effects caused by the primary beam. It is possible to use such a window as the angular distribution of the fission fragments is almost isotropic and the stopping effect of the foil on the fission fragments is negligible. The He gas flow, typically at a pressure of 200 torr (∼ 267 mbar), guides the fission products to the mass separator, through a 1.2 mm aperture in the exit nozzle, resulting in an evacuation time of a few tens of ms. The design of the stopping chamber is an important parameter of the measurements since it can affect both the extraction time and the stopping effi- ciencies. Since the time needed to evacuate the gas chamber is typically of the order of a few tens milliseconds, it is evident that the design of the fission guide generates a constrain in the ability of the method to measure properties

19 0 5 cm

Stopping chamber Target chamber

Fission products He gas

Ni foil natU Target Cyclotron beam Fig. 2.2. The IGISOL fission ion guide as it can be seen from the top, adapted from [24]. of short-lived nuclides. In fact of the whole experimental set up, the fission guide is the slowest component until the RFQ cooler and buncher. The stopping efficiency defines the fraction of products which are stopped inside the buffer gas. The produced fission fragments have a broad distribution of kinetic energies, so that the slowest ones cannot escape the target at all, while the ones with the highest kinetic energy implant into the walls of the ion guide. Only a fraction of the produced particles, those with the most appropriate energies can be thermalised in the gas volume. Although mass dependence of the stopping efficiency in the ion guide is expected to exist, such an effect has not been observed experimentally since its first indication was mentioned in [33]. Moreover, recent simulation studies on the stopping efficiency of the ion guide indicate that the systematic uncertainties due to the fission product mass and energy are small with a proper selection of target thickness, and that a nickel foil thickness of about 1 mg/cm2 results in a weak mass dependence in the stopping efficiency [24]. During the time the ions spend in the chamber, a limited number of chemical reactions can occur in the gas volume as deduced in [35], since the most important ionisation mechanism is the nuclear reaction itself. Hence, the ion guide can be used for the production of almost any isotope, so in that sense the technique is element independent. However, the efficiency of the ion guide is not expected to be the same for all elements, due to differences in the first ionisation potential, but the differences are expected to be small. As a proof of this, the deduced isobaric Z distributions from many works can be used ([15], [33], [34], [36]). These distributions resemble a Gaussian distribution

20 as expected, something which would not be the case if the efficiency of the ion guide was strongly dependent on the chemical properties of the ions. The total efficiency of the ion guide is the product of the stopping efficiency and the extraction efficiency. All stopped ions can not be extracted from the ion guide, due to interactions with walls, charge exchange reactions in the buffer gas and radioactive decays that lead to ion losses. As a result, the extraction efficiency reduces the total efficiency of the gas cell, and it has been measured at the upgraded IGISOL-4 to be 0.1% for 112Rh in proton-induced fission. As a comparison, it is worth mentioning that at IGISOL-3 the same efficiency was measured to be 0.02%.

2.2.2 Mass separator After the ions are extracted from the fission guide, they are guided to the dipole mass separator. There, the first selection of the ion beam takes place based on the charge over mass ratio (q/m). The desired ions are exiting the dipole magnet through a fixed 7 mm slit, aligned vertically with respect to the focal plane of the magnet. The trajectories of mass separated ion beams are handled with two electrostatic beam benders, where the first one is a parallel plate beam kicker, used to block the beam before the slit, so that the cooling cycle (tc) of the RFQ can be controlled, as will be discussed in the next section. The second electrostatic bender at 30° is used to deflect the ions to the RFQ.

2.2.3 Radio-Frequency cooler and buncher The capture of ions by the Penning Trap is more efficient if the separated ions have low energy and if the beam is bunched instead of continuous. Therefore, the ions are first cooled and bunched by a so-called radio-frequency cooler and buncher instrument (RFQ) [37]. The RFQ cooler and buncher is floating on a HV platform so that the ions are decelerated from 30 keV to about 100 eV. Inside the RFQ, there is a high purity (impurities of 10−5) helium gas at ∼10−2 mbar, in order to reduce the kinetic energy of the incoming ion beam, via collision with the atoms of the gas. The ions are accumulated inside the segmented linear radio-frequency quadrupole field. They are confined axially due to a dc potential applied to the segmented rods, while the applied quadrupole field creates the effective potential which guides the ions towards the symmetry axis of the RFQ. The kinetic energy of the ions is decreased to the level of the helium gas due to collision with it. Afterwards, the ions can be released in short bunches to the Penning Trap. A few ms are sufficient for the ions to cool down to eV levels, but the time spent by the ions in the RFQ (tc) is usually chosen to be equal

21 to the time the ions spend in the Penning Traps (tp), as will be explained in section 2.2.5.

2.2.4 Isobaric purification with JYFLTRAP The JYFLTRAP facility consists of a double longitudinal Penning Trap and was recently moved to the new location along with the IGISOL facility ([38], [39]). With the upgrade, new possibilities opened for the facility, such as separate beam lines for JYFLTRAP and the collinear laser spectroscopy station, located after the radio-frequency quadrupole cooler and buncher. In a Penning trap the ions are confined in two dimensions by applying a strong magnetic field (7 T in JYFLTRAP) parallel to the symmetry axis of the trap (~B = B~ez). By superimposing a static quadrupole potential in three or more cylindrical electrodes, confinement in three dimensions can be achieved in a small volume of about 1 cm3. The motion of an ion with mass m, charge q and velocity υ inside the trap is defined by the Lorenz force:

mr¨ = q(~E +~υ ×~B) (2.1) which leads to two radial oscillations at the angular frequencies ω+ and ω− and an axial motion at the angular frequency ωz: 1 q ω = (ω ± ω2 − 2ω2) (2.2) ± 2 c c z

r qU ω = 0 (2.3) z md2 where d is the characteristic trap dimension: s 1 r2 d = (z2 − 0 ) (2.4) 2 0 2 and ωc is the rotational frequency of the charged particle in absence of electric ﬁeld: q ω = B (2.5) c m The motion of the trapped ion can be represented by three eigenmotions to which the aforementioned frequencies correspond. The ion trajectory is visualised in Fig. 2.3. Particularly, the slow radial oscillation, with the frequency ν− is called the magnetron motion and the motion with frequency ν+ is called the reduced cyclotron motion. The motion with frequency νz takes place along the axis of the magnetic ﬁeld. The cyclotron frequency can be expressed as a combination of these three frequencies [40].

22 1.5 1 axial 0.5

0 -0.5 z -1 y reduced -1.5 cyclotron -2 x 1.5 1 magnetron 1.5 0.5 1 0 0.5 -0.5 0 -0.5 -1 -1 -1.5 -1.5

Fig. 2.3. The ion’s trajectory in the Penning trap, ﬁgure adapted from [41].

2 2 2 2 νc = ν+ + ν− + νz (2.6)

The purification of the ion beam occurs in the first trap, the purification trap, which was the only one that was used in the fission yields experiments. In order for the ions to enter into the first trap, the axial potential wall at the injection side is lowered below the kinetic energy of the ions. After the ion bunch arrives at the centre of the trap, the wall is restored, creating a potential minimum at the centre of the trap along the axial direction. The purification cycle of the bunch starts with cooling the ions through their collision with the Helium gas of 10−5 mbar with which the trap is filled. The amplitude of the fast motion (axial and the reduced cyclotron) is reduced, while the magnetron motion amplitude slowly increases, as a result of the repulsive effect by the electrostatic field. By applying a dipole excitation the magnetron radius of all ions, independent of their m/q ratio is increased further. In order to prevent the loss of the ions due to their interactions with the electrodes of the trap, a quadrupole excitation at the cyclotron frequency νc is applied, so that the magnetron motion is converted to the reduced cyclotron motion, and the ions, whose mass and charge satisfy Eq. 2.5 are re-centered. The conversion of magnetron radius to cyclotron is illustrated in Fig. 2.4. Then the axial potential wall on the extraction side is lowered, so that the ions are accelerated and directed through a 1.5 mm aperture to the MCP detector at the end of the

23 1.5 (a)

0.5

0 y / mm

−0.5

−1

−1.5 −1.5 −1 −0.5 0 0.5 1 1.5 x / mm

Fig. 2.4. The conversion of the magnetron motion to the cyclotron motion, figure adapted from [41]. beam line, after passing through the second trap (precision trap), which was not used in the fission yield experiments. The whole procedure, as described above, typically lasts a few hundred milliseconds, and is called the purification cycle, whose length is denoted as tp. This time is closely related to the mass resolution that can be obtained during an experiment, since longer purification results in better resolution. On the other hand longer purification time may incur decay losses of short-lived nuclei, so an optimisation of the cycle length should be achieved. The mass differences for adjacent members of an isobaric chain increases the further from the line of stability they are, but they decrease closer to the valley of stability or for isomeric states of the same isotope, so that a longer purification cycle is necessary. Although decay losses are not an issue for the former case, where the isotopes are stable or long-lived, they might need to be taken into account when isomeric states are measured. For the purposes of the current studies, the purification cycle was from 430 up to 660 ms. The mass resolving power which can be achieved by the Penning Trap is m/∆m ≈ 8·105, much higher than the respective one of the magnet separator. As explained earlier, the mass resolution depends on the purification time, so it is clear that the width of the observed mass peaks depends on these settings and it is not an attribute of the masses themselves. A parameter in the purification

24 length that plays an important role is the cooling time. A longer one results in a better centring efﬁciency of the trapped ions of the desired masses, thus improving the mass resolution and the transmission efﬁciency of the trap.

2.2.5 Timing Structure of the measurement Figure 2.5 illustrates the timing structure of the performed experiments. The most time consuming part of the procedure is the purification cycle tc in the Penning Trap. By executing in parallel the preparation and the purification cycle the time required for the experiments is reduced by half. As can been noticed in the figure, the preparation cycle (tb + tc) is set equal to the purification cycle tp, so that a new bunch in the RFQ cooler and buncher is prepared, while the preceding one is purified in the trap. The space charge limit of the Penning Trap sets one more constrain to the size of the bunch, since this should not be too big in order to avoid such effects. The amount of the ions inside the trap could be reduced by simply lowering the cyclotron beam intensity, as in this case the yield of the long-lived species, which are produced at higher rates and they actually cause the space charge effects, would be decreased. How- ever, this would keep the yield of the short-lived, less produced isotopes at a non-measurable level. Moreover, by adjusting the cooling cycle of the RFQ, the fraction of short-lived isotopes after the purification is enhanced, as in this way the decay losses of short-lived isotopes in the RFQ are minimised. If the cooling cycle is set rather long, the decay-losses would be increased, while the long-lived species would keep on accumulating in the RFQ. Thus a short tc and intense cyclotron beam is considered the optimal setting. For each isobaric chain, a frequency scan was performed, which means that the cyclotron frequency νc was applied over the mass of interest. The events were detected by a MCP detector, located at the end of the beam line, after the Penning Trap, and the events were recorded together with the applied frequency scan, as will be explained in section 3. The frequency scan was repeated several times, in order to acquire adequate statistics, and the number of these scans were varying in each case from 5 to 233.

25 RFQ TRAP ions blocked to enter RFQ

ions collected to RFQ tb tc tp

Bunch # N-1 ions puriﬁed in Penning Trap

RFQ TRAP

tb tc tp Bunch # N

RFQ TRAP

tb tc tp Bunch # N+1

total cycle time

TIME

Fig. 2.5. The selected puriﬁcation cycle length tp dictates the timing of the experiment. While an ion bunch is puriﬁed in the Penning trap, the next bunch is prepared in the RFQ.

2.3 Chemical effects of IGISOL and JYFLTRAP Even though the IGISOL method is claimed to be chemically non-selective, this does not mean that it is completely free of chemical reactions. There are certain places along the beam line, such as the fission guide and the Penning Trap, where chemical reactions may occur. Their occurrence and significance depend on the number of impurities and on the time the ions spend in these specific environments. As explained in section 2.2.1, the evacuation time of fragments is similar for all produced isotopes of an element and the impurities are at a constant, very low level. Nevertheless, since in the ion guide impurity levels below sub-parts-per-billion are required, a completely new gas purification and gas transport system has been constructed at IGISOL-4, as described in [27]. Another place which is filled with helium gas is the JYFLTRAP. Even though the gas pressure, and the impurities are much lower compared to the ion guide, the ions spend about ten times longer time here than in the ion guide. Some reactive elements, like Zr and Y thus have sufficient time, to produce molecules during the purification cycle. Charge exchange reactions between the ion and the impurity atoms may occur as well. This concerns mainly elements with a high first ionisation potential, such as Kr and Xe, so that weakly bound electrons of the impurity atoms may be captured by the ions of these elements, resulting in their neutralisation. As can easily be un- derstood, the buffer gas is the main source of impurities in the system, while it is also very essential for the operation of the RFQ and JYFLTRAP. Although

26 chemical reactions can not be fully avoided, one way to overcome this issue, is to perform relative measurements instead of determining absolute yields.

3. Data Analysis

The data of this work were acquired with two different methods. The IGISOL technique was employed in all experimental campaigns, while in June 2013 the yields of the products were also measured by means of γ-spectroscopy. In this section the analysis which was developed and followed in order to deduce the isomeric yield ratios from both methods is presented.

3.1 Penning Trap Data The obtained data is a result of several experimental campaigns, that took place from April 2010 until May 2014. The ﬁrst performed measurement was con- cerning the proton induced ﬁssion of Thorium, and it took place at IGISOL-3. Since then the facility was upgraded to IGISOL-4, as described in chapter 2, and the rest of the experiments were performed in the completely renewed facility. In the following table the date of the performed experiments are summarised together with the status of the facility at that time.

Experimental Runs April 2010 IGISOL-3 p - Th April 2014 IGISOL-4 June 2013 IGISOL-4 p - U August 2013 IGISOL-4 May 2014 IGISOL-4

Table 3.1. Kind and date of the experiments performed for this work.

The analysis of the data acquired from JYFLTRAP (mass purified data) is a multistep procedure, consisting of processes such as the spectra generation, the selection of desired events based on their time of flight, the analysis of the chosen ones by the counts-in-peak method and finally the corrections of the calculated yield due to radioactive decay. These steps are described in detail in the following sections. Each saved data file contains information about the time and the settings of the experimental run. Specifically, in the recorded file there is information regarding the scanning frequency, the Time of Flight (TOF) and number of counts for every detected ion.

29 3.1.1 Time of flight selection The ions leave the purification trap with the same energy, so their Time Of Flight (TOF) depends only on the mass. This results in one peak in the TOF distribution, which can be distinguished easily, and by gating on this peak a selection only of the desired events can be achieved so that only these will be used for the later analysis. In this way, random noise that is registered in the MCP detector, and appear in the time of flight spectrum as small peaks or as randomly distributed events, can be eliminated. These events are generated either by false triggers of the detector or by discharging sparks of real ions from JYFLTRAP. However they can be treated as background noise since they do not belong to the elements that are aimed to be measured. A TOF distribution spectrum is depicted in Fig. 3.1, where the coloured peak, which corresponds to the TOF of the masses of interest, is clearly seen. The vertical lines on each side of the peak defines the gate on the distribution, so that only events within this specific time of flight range will be analysed. By gating on the TOF distribution a background subtraction can be achieved, which in most cases is sufficient and no further background reduction is needed.

Time Of Flight

103 Counts

102

0 100 200 300 400 500 Time Of Flight (µs)

Fig. 3.1. Time of Flight distribution of mass A=96. The red lines depicts the events that were selected to be further analysed.

In Fig. 3.2, the contribution of the TOF gating on the background subtraction can be noticed. In (a), the raw frequency spectrum is presented, before any TOF gating and thus background subtraction, while in (b), the same mass

30 spectrum after gating on the most prominent peak on the TOF distribution spectrum is depicted.

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 3 ×10 Frequency [kHz] 140 (a) 120 100 80 60 40 20

1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 3 ×10 01120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 140 120 (b) 100 80 60

Counts 40 20 Sr 3 3 1120.3 1120.32 1120.34 1120.36mY 1120.38Y 1120.4×10×10 1201120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 10 (c) 8 6 4 2 3 0 ×10 1120.3 1120.32 1120.34 1120.36 1120.38 1120.4

Fig. 3.2. The effect of the TOF gating on the background subtraction on a frequency spectrum is visualised. In (a), the black histogram represents the frequency spectrum of mass A=96 without any background subtraction, while the red histogram shows the events after the TOF gating. In (b) the same mass spectrum, but only after the TOF gating is shown and in (c) the background events are depicted.

3.1.2 Peak intensity determination In order to calculate the isomeric yield ratios, the intensity of the peaks in the frequency spectrum had to be deduced and then compared to each other. For the identification of the masses appearing in the spectrum, a cyclotron frequency calibration based on the evaluated atomic masses was used [42]. The height of the mass peak can be considered as a direct measurement of the beam intensity since the maximum transmission efficiency is achieved at the cyclotron frequency. By fitting a gaussian function to these peaks, their height can be calculated. In the Penning trap spectrometer, the shape of the mass peak is not uniform for all cases, but it strongly depends on the settings of the trap. However, in our case, the approach of a gaussian function with certain constraints can be considered adequate, especially since a number of criteria are fulfilled. The shape and the width of the peaks are believed to be invariant for given settings, so that the peak area and height can both equally represent the beam intensity. Therefore the number of counts is possible to

31 be used for the extraction of the yield ratio, since both the nominator and the denominator in the fraction are estimated from the same experiment. In the present work, all the ﬁts were performed by applying gaussian functions on the experimental peaks. Speciﬁcally, a function consisting of the same number of gaussian functions as the number of the peaks in the spectrum was created. One condition for this function was the width of the peaks to be the same for all masses, since this represents the detection resolution, which is related to the applied quadrupole excitation of the Penning Trap, as has already been explained in subsection 2.2.4. For example, in a case with three peaks we create a function which consists of three gaussian curves as shown in Eq. 3.1.

2 2 (x − xre f ) (x − xisom) G1(x) = A1 · exp(− 2 ) + A2 · exp(− 2 ) 2σ 2σ (3.1) 2 (x − xgs) + A · exp(− ) 3 2σ 2 where A1, A2 and A3 stand for the height of each peak. A problem that arises from the analysis is where to define the peak positions, especially since we are interested in isomeric states, which most of the times are lying very close to the ground state, and thus they overlap. For the exact position of the peaks, which are depicted as xre f , xisom and xgs in the above equation, we take advantage of the fact that in the measured spectra there is at least one isolated and well defined peak, which corresponds to a known mass. This mass is usually the precursor (or the daughter) of the nuclide of interest, before (or after) its β-decay. This peak is taken as the xre f and since the masses are adequately known, at least enough for our purpose, in order to define the position of the isomeric state we are making use of the following equation:

xisom × misom = xre f × mre f (3.2) and by solving it for xisom, we have that

mre f xisom = × xre f (3.3) misom It is evident that the position of the peaks in the spectrum are deﬁned relative to their standard distance from the isolated peak, reducing this way the number of the unknown parameters in Eq. 3.1 to ﬁve, and resulting in:

misom 2 2 (x − · xre f ) (x − xre f ) mre f G(x) = A1 · exp(− 2 ) + A2 · exp(− 2 ) 2σ 2σ (3.4) mgs 2 (x − m · xre f ) + A · exp(− re f ) 3 2σ 2 32 In cases where more than three peaks were present in the spectrum, a procedure similar to the one described above was followed, with the only difference that the G1(x) consisted of more than three gaussian functions. In all cases the reference point was taken from the best defined peak in the spectrum. The intensity of each peak was calculated afterwards by integrating a gaussian function on each peak. For the values of the parameters of the new defined gaussian, the values of the fitted peaks were used, managing this way each of the peak to have the same width. It is not necessary that the peak width has the same value for the measurements of all experiments, as has been already described, since the achieved resolution strongly depends on the settings of the Penning Trap. It is sufficient as far as it stays constant for the same measurement, and as quality assurance it is desired that the σ of the gaussian to be similar for similar settings of the trap. In Fig. 3.3 an example of a frequency distribution is illustrated after the TOF gating. The red dashed line represents the gaussian fitted function G(x), which in this specific case consists of three gaussians.

A=96

140 Counts 120

100

20 Sr mY Y

3 0 ×10 1120.3 1120.31 1120.32 1120.33 1120.34 1120.35 1120.36 1120.37 1120.38 1120.39 1120.4 Frequency [kHz] Fig. 3.3. Frequency distribution spectrum of mass A=96. The peak positions of 96mY and 96Y are calculated relative to 96Sr, which is taken as reference. The peak identiﬁcation is based on a frequency to mass calibration. The red dashed line shows the gaussian ﬁtted function G(x).

33 3.1.3 Corrections due to radioactivity The ions travel the distance from their creation in the IGISOL chamber to their detection in the JYFLTRAP, typically in some hundreds of ms, so during this travel path some losses due to radioactive decays will occur. The ions spend about 90% of this time mainly in the RFQ and the traps, so radioactive decays are most likely to happen there. There are three potential ways in which radioactive decays can affect a measurement: • β-decay daughters can be released from the surfaces of the IGISOL front-end (i.e the walls of the ion guide and the surfaces of the SPIG electrodes.). • β-decay products can be captured in the trap. • decay losses because of the radioactive decays from short-lived nuclides. Due to the nature of the fission reaction and the settings of the traps, the contribution of the first two factors, for different reasons in each case, is not very significant, as it has been investigated and described in detail in previous works [31], [43]. Specifically the overall transmission efficiency of JYFLTRAP is ∼0.01%, so a lot of ions are either lost in the ion guide or are extracted as neutral or multiple charged ions. It has been studied thoroughly, that even in the worst case the contribution to the yield of the isotope of interest due to the release of β-decay products does not exceed 1%. The contribution of the β-decay that can be captured in the trap and thus dis- turb the observed yield of the nuclide of interest is expected to be small, if not negligible. This happens because of the nature of fission, and due to the very short time of the purification cycle, which is usually of the order of ms. Hence, only very exotic isotopes can decay during these times, but their fission cross sections decrease rapidly towards the very exotic area of the neutron rich isotopes, approximately about a factor of ten per mass unit. Since this production ratio is very small, it is expected that even if all decay products were trapped, this would increase the measured yield of about 10%. The decays of the most produced to the less abundant and stable isotopes can be ignored, since this is unlikely to happen due to their long half-lives. Since fission produces isotopes on the neutron rich side of the chart of nuclide, a possible β-decay will result in a doubly charged ion, because of the change of the nuclear charge. The Pen- ning Trap is tuned though for single charged particles, so even if the β-decay products will be trapped, they will be eliminated in the purification cycle.

Decay losses due to radioactive decays As already mentioned, the ions spend most of their time from their creation to their detection in the MCP, in the RFQ and the Penning Trap, so this is the only time that needs to be taken into account in order to apply corrections for losses due to radioactive decays within these two apparatuses. The evacuation time from the ion guide is rather short and it can be neglected for these corrections. Thus, the correction function consists of two components, one for the

34 radioactive decays that occur during the preparation cycle tc of the RFQ, and the other due to the decays during the purification cycle tp of the Penning Trap. In the current experiments these two times were equal, but they were varying from 430 up to 660 ms depending on the experiment. Short-lived nuclides will decay during this time interval, so corrections due to the decays are considered to be important especially for the most short-lived ones. The detected number of ions N of a certain nuclide is taken to be proportional to the initial number of ions N0, that are extracted from the ion guide, in case the transmission and the detection efficiency are excluded. Then the ions are assumed to enter the RFQ at a constant rate N0/tc, which is equal to a typical radioactive growth-in period, expressed by the first term in Eq. 3.5. Afterwards, a bunch of ions are ejected from the cooler and enter in the trap, and only ions that decay in the traps during the purification cycle tp are lost. These losses are expressed by the second term of Eq. 3.5. The equation that can be applied for these corrections is: N N = 0 · (1 − e−λtc ) · e−λtp (3.5) tcλ where λ is the decay constant of the nuclide. A part of the above equation can be taken as the correction function ψ, which depends on the decay constant λ: eλtp ψ(λ) = tcλ · (3.6) 1 − e−λtc so that the relation between N and N0 can be expressed as: N 0 = ψ(λ) (3.7) N The uncertainty of the corrected mass peak intensity is given by: s ∆N ∆N 2 ∆ψ(λ)2 0 = + (3.8) N0 N ψ(λ) where the first factor represents the statistical uncertainty of the peak intensity, and the second one the uncertainty of the correction function ψ, which is a function of the half-life of the measured isotope. The statistical uncertainty ∆N can be calculated from the experimental data. The uncertainty of ∆ψ can be estimated from the uncertainty of the decay constant λ of the nuclide of interest and the derivative of ψ: ∆ψ(λ) = ∆λ · ψ0(λ) (3.9) where, the uncertainty of λ is calculated from the half-lives taken from the Nubase2012 evaluation of nuclear properties tables [42], and the derivative of ψ is: 0 tc −(tc+tp)λ 1 ψ = e − tp + (3.10) λ λ

35 In the present study, the decay corrections were applied whenever the half- lives of the nuclides were smaller than ten times the purification cycle length tp. The decay correction function ψ(λ) decreases monotonically with half-life, where longer half-lives correspond to smaller correction and shorter half-lives to bigger ones. It is thus easier, instead of computing the uncertainty of the corrections function with algorithms, to deduce this uncertainty by the upper and lower limits [43]. This uncertainty is expected to be asymmetric and more pronounced for the short-lived nuclides, because of the non-linearity of the correction function ψ(λ). A symmetric approximation of the uncertainties were considered to be sufficient though for the present work, since the half-lives of the detected nuclides were, in the worst case comparable to the sum of the cooling and purification time. Therefore the correction function’s uncertainty is calculated by symmetric intervals of the average value of ψ(λ), as follow:

∆ψ(λ)avg = (ψ(λ + ∆λ) + ψ(λ − ∆λ))/2 (3.11) For the calculation of ψ(λ +∆λ) and ψ(λ −∆λ) in the above equation λ was substituted with (λ + ∆λ) and (λ − ∆λ) respectively in Eq. 3.6.

3.2 γ-spectroscopy Data In parallel with the Penning trap measurements in June 2013, γ-spectroscopy data for the same isobaric chains were taken as well by using a HPGe detector, so that the results from the two different experimental techniques can be compared to each other, and thus the consistency of the upgraded facility evaluated. The secondary produced beam is separated with a 55° dipole magnet resulting in the selection of an isobaric chain with the desired mass number A. As already mentioned a mass separation at the order of m/∆m = 500 can be achieved from the magnetic dipole magnet. After the separation, the electrostatic switchyard is turned to a dedicated γ-spectroscopy setup, so that the beam instead of proceeding to the RFQ cooler and the JYFLTRAP, will be transported to the spectroscopic station. The ions are implanted in an alu- minium foil, placed in front of the detector, so that γ-ray data can be collected on-line for several hours. This technique can be applied to all short-lived ﬁs- sion products with know γ-ray intensity and decay constants. The constraints of this method regard the cases where the products are stable, or they decay without γ-ray emission, or their intensities or half-lives are not well known. For the analysis of the acquired spectra the code TV, developed at the University of Cologne (Germany), was used ([44]). The intensity of the desired peaks was calculated by performing a gaussian ﬁt. In each case and before every measurement, the background activity was recorded and afterwards subtracted from the spectrum of interest. By doing this, the reduction of the buildup of long-lived activities along the beam line ("instrumental background") could be achieved. The γ-rays that were used for the determination

36 of the isomeric yield ratios are presented in Tab. 3.2, together with their decay probabilities and their half-lives. In the table, only the most intense γ-ray of each nuclide is written. If more than one γ-ray could be determined quantitatively, the yield is calculated from the weighted average of all considered γ-rays.

Mass Nuclide Eγ (keV) Iγ (%) T1/2 (sec) Nuclear Library

81 31Ga 216.8 37.4 1.22 [45] m 32Ge 2174.3 6.3 7.6 [45] 32Ge 1495.5 19.9 7.6 [46] 97 38Sr 1905.0 25 0.43 [45] m 39Y 161.4 72.5 1.17 [46] 39Y 3287.6 18.1 3.75 [46] m 41Nb 743.5 100 58.7 [46] 41Nb 657.9 98.2 4326 [46] 128 49In 2104.1 6.5 0.845 [46] m 50Sr 831.5 100 6.5 [46] 50Sr 482.3 59 4744 [46] m 130 50Sr 144.9 23 102 [46] 50Sr 780.4 56.4 223.2 [46] Table 3.2. Nuclear data used for the analysis and the deduced isomeric yield ratios. Only a main characteristic γ-ray of each nuclide is listed.

meas The determined intensity (Yγ (A,Z))) of each peak, had to be corrected for its intensity (Iγ ) and for the efﬁciency (ε(Eγ )) of the HPGe detector for this speciﬁc energy.

meas corr Yγ (A,Z) Yγ (A,Z) = (3.12) Iγ · ε(Eγ ) The intensity of each γ-ray, as well as the half-lives of the isotopes, were taken from the evaluated libraries, explicitly mentioned in Tab. 3.2 for each case. In Fig. 3.4, the γ-ray spectrum of mass A=128 is presented, where the γ- rays that were used for the analysis and some of the most intense that appear in the spectrum are marked.

3.2.1 Efficiency calibration In order to be able to identify the observed γ-rays, an energy calibration using a 60Co source was performed, before deducing the efficiency of the detector. The calibration was valid for all measurements, since the electronic settings of the detector stayed the same throughout the experiment. The energy resolution of the detector was measured to be 2.63 keV at 1173 keV and 2.72 keV at 1332 keV. To extract the intrinsic efficiency of the detector, a 152Eu source was used. The source was placed at the low-background measurement station, in order

37 Α=128 100

90 Sb, mSb

70 mSn Intensity (cps)

60 mIn, mSn Sb

50 Sn

40 Sn

In Sn

20 Sn

mSn In

0 0 500 1000 1500 2000 2500 Energy (keV)

Fig. 3.4. γ-ray spectrum of mass A=128, as obtained during the experiment. In the spectrum, the peaks, both of the parent and the daughter nucleus, that were used for the analysis are marked. Some of the most intense γ-rays emitted from other nuclides of the mass chain are labeled as well.

to avoid contamination from the surrounding materials. By placing the source far enough from the detector and at a low background activity area, the un- wanted summing coincidence events could be avoided. The source covers the energy range from 120 keV to 1500 keV, essentially covering the energy range of relevance for the fission products that were measured during the current experiment. In order to extract the efficiency curve the experimental data were fitted using a polynomial fit in ln(ε) against ln(Eγ ) by applying the following

38 formula: N i−1 ln(ε) = ∑ ai[ln(Eγ )] (3.13) i=1 where Eγ is the γ-ray energy, ε the full energy peak efficiency and αi coeffi- cients which are determined by the fitting algorithm. Since the energy range was constantly above the "knee", a polynomial of the same order was used for all cases (N=4). The resulting efficiency curve is depicted in Fig. 3.5.

Full•energy Peak Efficiency Calibration 0.08 0.07 0.06 Efficiency 0.05 0.04

0.03

0.02

200 300 400 500 1000 Energy (keV)

Fig. 3.5. The calculated intrinsic efﬁciency of the HPGe detector, with a conﬁdence interval of 95%.

3.2.2 Decay corrections corr Yγ is given by Eq. 3.12 and can be related to the number of ﬁssion products of each nuclide (A,Z), that are formed at time t after the beginning of the implantation on the foil by the following equation:

T Zmeas corr Yγ = λ(A,Z) · N(A,Z)dt (3.14) 0 where Tmeas is the measuring time, which in our case was the same as the irradiation time.

39 Through Bateman’s equation the partial independent yield can be extracted from the measured activities, which are given by the number of the ﬁssion products that arrive to the foil from the target. In general, the number of nuclei Ni for the characteristic decay constants λi at a time t are given by equations (3.15)-(3.16): dN 1 = −N λ (3.15) dt 1 1

dNi = −N λ − N λ , i = 2,3,... (3.16) dt i−1 i−1 i i Solving these differentials equations the activities can be obtained as follow:

A1 = A10 exp(−λ1t) (3.17)

λ2 A2 = A10 {exp(−λ1t) − exp(−λ2t)} + A20 exp(−λ2t) (3.18) λ2 − λ1

A3 = ... (3.19) Equation (3.17) gives the activity of the nuclide when there are no precursors or the contributions of the precursors to the yield are negligible, or the γ-rays emitted by the parent nuclei are so weak that are impossible to be measured. In case the contribution of the precursor is considered to be significant, so that it has to be taken into account, equation (3.17) gives the activity of the precursor and equation (3.18) expresses the radioactivity of the daughter nuclide, when there is only one precursor. In case there are contributions from more than one precursor equation (3.16) can be solved for as many precursors as are required. Due to the nature of fission, as already explained in the previous section, there is a significant difference in the production rate distribution for the same mass number A, when moving from nuclide with (A,Z − 1) to (A,Z). Therefore corrections of the yields due to contribution from precursors, if any, were restricted to the cases with just one precursor. More on this, depending specifically on each case, can be found in chapter 4, where the results of the current work are presented. In the current case, where fission products were constantly produced, the obtained activities at the end of the collection can be converted to corresponding cross sections, taking into account approximations that need to be applied for saturation conditions. Thus the differential equations (3.15)-(3.16) become: dN 1 = N σ ε φ − N λ (3.20) dt 0 1 1 1 1

dNi = N σ ε φ + N λ − N λ , i = 2,3,... (3.21) dt 0 i i i−1 i−1 i i 40 where N0 is the number of the target nuclei, σi represents the cross sections, εi is the transport efﬁciencies in IGISOL for each nuclide, and φ is the proton beam ﬂux. By solving these differential equations and afterwards by integrating over the collection time T, which in this particular case was equal to the irradiation time, the activities A10, A20,... at the end of the collection can be extracted: h 1 i A10 = N0σ1ε1φ T − {1 − exp(−λ1t)} (3.22) λ1

h λ2 λ1 A20 = N0σ1ε1φ T− {1 − exp(−λ1t)} − {1 − exp(−λ2t)} λ1(λ2 − λ1) λ2(λ1 − λ2) h 1 i + N0σ2ε2φ T − {1 − exp(−λ2t)} λ2 (3.23) In the general case of equations (3.22)-(3.23), the quantity of radionuclide increases during irradiation and then decreases by radioactive decay over the measurement time. The increase of the radioactivity can reach a maximum value. It is expressed by the "approach to saturation" factor {1 − exp(−λitirr)}, where tirr is the time while the target was being irradiated. After the saturated activity level of a nuclide has been reached no further increase in it can be achieved. For the current experiment the irradiation time was the same as the measuring time, since the activity was being registered on-line, while the target was being irradiated. The data were being acquired for a much longer time than the half-lives of the measured isotopes, so it could be assumed that the former factor is equal to one {1 − exp(−λitirr)}=1 , meaning that the maximum activity has been reached in all but one case. The only case where this did not happen was the 128Sn case, whose half-life of the ground state is 59.07 min. The irradiation time was equal to the half-live, so the former factor could be approximated to half of the maximum activity [47]. Equations (3.22)-(3.23) give the number of disintegrations during the irradiation time, since they are the products of the integrated maximum activity reached over this time, identical to the right part of equation (3.14). For the analysis the branching ratio of these disintegrations were always being taken into account whenever possible. By combining equations (3.22),(3.23) and (3.14) the relative independent yields of the nuclides of interest in the form of N0σ1ε1φ can be deduced. In equations (3.17)-(3.18) the factor exp(−λit) expresses the normal radioactive decay of a nuclide that occur as long as γ-decay data are registered, considering that this takes place after ﬁnishing the target irradiation. However, in this particular case this factor can be taken equal to one, since irradiation and data acquiring were happening in parallel.

41 3.2.3 Transport efficiency In the relative independent yield mentioned above, the transport efficiency ε of the nuclide is included. Even though this can differ element by element, in the case of the isomeric yield ratio it will cancel out since it contains the population of two different levels of the same nuclide. Specifically the overall transport efficiency of IGISOL can be regarded as the product of the physical transport efficiency εp and the chemical transport efficiency εc. The physical transport efficiency depends on the operating conditions of the mass separator, such as the width of the slit, while the chemical efficiency is related to the chemical properties of the elements [15]. As the members of a given isobar are measured simultaneously, it is evident that the transport efficiency εp is the same. The chemical efficiency though depends on the charge Z1 and Z2 of the isobars, and in principle can play a role in the correction for decay contributions from the precursors. However, this is expected to be small, especially since in most cases the produced yield of the precursors is very lower compared to the yields of the nuclides of interest.

3.2.4 Uncertainties The total uncertainty is given by the following equation:

q 2 2 ∆tot = ∆stat + ∆Decay (3.24) where each component is described in the text below:

Statistical uncertainties ∆stat The statistical uncertainty was calculated by error propagation on Eq. 3.12. The γ-ray data were analysed with the help of the code TV. A gaussian fit was performed on the selected peaks so that the area within this peak is deduced, only after the background of each peak was subtracted. The uncertainty of the integration is given by the program itself. The uncertainty due to the detection efficiency is deduced from the weighted fit which performed on the experimental data, as illustrated in Fig. 3.5. Uncertainties in the intensities of the γ-rays can be found in the nuclear libraries from which the data were taken. The library used for each nuclide is shown in Tab. 3.2.

Uncertainties due to decay of parent nuclei ∆Decay As can be noticed in equations (3.20) and (3.21), the uncertainty due to the β-decay of the mother nucleus has to be propagated to the uncertainty of the daughter nucleus yield, whenever such yield corrections were performed. It was calculated by summing the uncertainties of the efﬁciency and the intensity of the mother nucleus, weighted by the ratio of the detected mother and daughter nuclei.

42 4. Results and Discussion

4.1 Presentation of the results In this section the isomeric yield ratios of six isomeric-ground state pairs in a wide mass range (from A=81 to A=130), produced from the proton-induced fission of natU and natTh are presented. As mentioned in chapter 3, the experiments were performed in different campaigns. In all cases, the fission was induced by a proton beam at 25 MeV. The fission products, after being isobarically separated, were measured with two different methods. With both targets, the yields were measured by employing the Penning Trap, so that close lying isomers could be separated and detected by the Multi Channel Plate located at the end of the beam line. With this method, direct counting of the fission products can be performed for both the ground and the isomeric state of a given nuclide, thus allowing the determination of the isomeric fission yield ratios. In June 2013 though, in one of the first experimental runs after the recommissioning of IGISOL and JYFLTRAP, in addition to employing the Penning Trap, the fission products were also measured by means of γ-spectroscopy, in order to evaluate the consistency of the upgraded facility. In this measurement only the natU target was used.

Ground State Isomeric State

Nuclide Z N Spin τ1/2 (s) Eexc (keV) Spin τ1/2 (s) Decay Mode 81Ge 32 49 9/2+ 7.6 679 1/2+ 7.6 β −∼100%, IT<1% 96Y 39 57 0− 5.34 1140 8+ 9.6 β −∼100% 97Y 39 58 1/2− 3.75 667 9/2+ 1.17 β −>99.3%, IT<0.7% 97Nb 41 56 9/2+ 4326 743 1/2− 58.7 IT=100% 128Sn 50 78 0+ 3544 2091 7− 6.5 IT=100% 130Sn 50 80 0+ 223.2 1946 7− 102 β −=100% Table 4.1. Information of the states for the nuclides measured in this work.

In Tab. 4.1 information regarding the mass number (A) and atomic number (Z) of each nuclide is presented, together with the spins and the energies of the ground state and metastable levels. The decay mode of the isomeric state is also mentioned in the table and as can be noticed, in most cases β-decay is the dominant one. The decay mode of the ground state is not shown in Tab. 4.1, since in all cases it occurs by β-particle emission, as all nuclides measured in this work are located away from the valley of stability, on the neutron rich side. In Tab. 4.2 the results are presented in the form of ratios of the isomeric yield over the ground state yield. As can be noticed in the table, there are

43 three different runs that were performed with the Uranium target, in June and August 2013 and in May 2014, while there are two different measurements with the Thorium target. One was performed in April 2010 at IGISOL-3 facility, viz before the facility’s major upgrade, and one in April 2014, at IGISOL-4. In the last column of the table, the available data in the literature are also presented. Empty cells in the table means that no measurement for that speciﬁc nuclide was realised, or that the spectrum was unclear.

Nuclide Yisom/Ygs nat Uranium nat Thorium nat Uranium June 2013 June 2013a August 2013 May 2014 April 2010b April 2014 Tanikawaa [36] 81Ge 0.04±0.01 0.59±0.13 0.08±0.02 0.15±0.03c 0.07±0.01 96Y 0.97±0.03 1.13±0.07 1.66±0.13 1.40±0.04 97Y 2.79±0.37 2.36±0.13 2.59±0.14 4.51±0.43 2.39±0.36 97Nb 0.30±0.03 0.27±0.01 128Sn 0.86±0.13 0.98±0.03 1.09±0.07 130Sn 0.89±0.31c 1.01±0.06 1.01±0.08 0.64±0.08 0.52±0.02 aperformed by means of γ-spectroscopy bperformed at IGISOL-3, all the other measurements were performed at IGISOL-4 comitted due to contamination in the spectrum, for more information see sections 4.2.1, 4.2.5 Table 4.2. Isomeric yield ratios of proton-induced ﬁssion on nat U and nat Th.

The statistical uncertainties for the Penning trap data are between 3% and 25%, while they are between 6% and 28% for the γ-spectroscopy. In the cases where more than one measurement was performed for the same mass in the same experiment, the ﬁnal value was taken as the weighted mean of the results.

4.2 Discussion and comparison In this section, the results obtained from the various experiments are discussed and compared to each other, while comparison with data existing in the literature is performed whenever possible. The comparison in this section is first performed for results obtained from the same target and the same method. If such data do not exist, then isomeric ratios deduced from the same target, but with different methods, are compared to each other. If even this is not possible, then comparison of the same produced isomeric pairs measured with the same method, but originating from a different fissioning system is realised. The comparison of isomeric yield ratios from different fissioning systems is a delicate situation. It is claimed, in general, that the population of the isomeric states is much more related to the nuclear properties of the individ- ual products, than to the dynamics of the fission process. Nevertheless, the probability of populating a certain isomeric level depends, even weakly, on the nature and the excitation energy of the fissioning system. As explained in the introduction section 1.2, the primary fragments can follow different decay paths due to the differences in the excitation energy and angular momenta. In

44 this work, some indications of the dependence on the fissioning system have been observed and are presented in the follow subsections. In Fig. 4.1 the results from the current study are presented. As can be noticed, the data points of some cases seem to be in better accordance than others. The agreement though, does not seem to follow a clear pattern. It should be mentioned that the uncertainties might be slightly underestimated as the systematic ones have not yet been determined quantitatively and included in the total uncertainty. In the following subsections, each case is discussed individually. The results are also compared with data available in the literature, and the comparison is presented in Fig. 4.1. In general, the available data of isomeric yield ratios in the literature are very scarce. As can be noticed in Tab. 4.2, the only work that has been performed in the past with common isomeric ratios as in the present study is the experiment by Tanikawa et al [36], whereas some of the isomeric pairs of the present work were observed for the first time. Tanikawa’s measurement was performed at the Tohuku IGISOL in 1993, with a method very similar to the one employed here. Specifically, the isomeric yield ratios of proton-induced fission on 238U at 24 MeV were measured, by means of γ-spectroscopy.

81 96 5 97 Ge 1.8 Y Y 0.6 1.6 4

0.4 1.4

3 1.2 0.2

1.0 97 128 130 0.35 Nb Sn 1.0 Sn 1.2

0.30 1.0 0.5 U • 6/2013 U • 6/2013 (γ) 0.8 U • 8/2013 U • 2014 Th • 2010 Th • 2014 0.25 Tanikawa

Fig. 4.1. In the ﬁgure, the isomeric yield ratios as deduced from the current work are presented. Results available in the literature are also shown.

45 4.2.1 Mass 81 The isomeric yield ratio of 81Ge was measured in all but one experimental campaigns, and it can be considered as the most difficult case for both methods. This can be verified from the big uncertainties, which actually are the largest ones of all cases. The isomer is separated by 679 keV, and it can barely be distinguished from the ground state peak using the Penning Trap, as is shown in Fig. 4.2, since this value is very close to the maximum resolving power of the purification trap. For this case a longer purification cycle could possibly be applied, so that a better separation would be achieved, since the half-lives are long enough, 7.6 sec for both the ground state and the isomeric state. The maximum purification cycle applied for these measurements was 510 ms. The result from the experiment with U in 2014 may be ignored, since some additional peaks were observed in the spectrum, most likely due to impurities in the buffer gas, which formed molecules in the Penning Trap. For the γ-spectroscopy data, the relative uncertainties are at similar levels, as in the Penning Trap data. This arises from the uncertainty in the yield of the isomeric state, mainly as a result of the large uncertainties - up to 18% - in the γ-ray intensities. The obtained spectrum is depicted in Fig. 4.3. The results from the Penning Trap for the case of the same target (U) do not agree with each other within uncertainties, but this is most likely due to their underestimation in the absence of the systematic uncertainties. The yield ratio of the measurement performed with Th target is identical to the one performed with U, in August 2013. The ratio deduced by means of γ-spectroscopy is very different than any other result for 81Ge.

46 A=81

20 Counts mGe Ge As 18

0 1327820 1327840 1327860 1327880 1327900 1327920 1327940 1327960 1327980 1328000 Frequency (Hz)

Fig. 4.2. Frequency spectrum for mass A=81 from 25 MeV protons on nat U. With the dashed vertical black lines, the position of the nuclides are marked based on their masses. A=81 18 As

16 Ge, mGe Ge, 14

Intensity (cps) 12

mGe

Ge As

8 Ga

Ge Ge 6

4 mGe mGe 2

0 0 500 1000 1500 2000 2500 Energy (keV)

Fig. 4.3. γ-ray spectrum for mass A=81, where the peaks used for the extractions of the yield ratio are marked. Some intense peaks of other nuclides from the mass chain are also labeled. 47 4.2.2 Mass 96 For this mass the yield ratio of 96Y could be extracted only from the Penning Trap data, since the ground state does not emit any γ-ray of significant intensity which could be used for the analysis. It is worth mentioning that this case is rather unique in the present study, since the isomeric state is produced, and consequently defined quantitatively, only in fission. For each fissioning system, two measurements were performed. The results from the same target agree within ∼15%, although not within the uncertainties which, as mentioned before, only include the statistical error. It should be noted that the isomeric ratios from the natTh target are higher than those from the natU target.

Multiple values for the same mass In some cases the same isomeric pair was measured several times in the same experiment. Whenever this occurred the weighted mean was calculated for the final value of the yield ratio. 96Y is such a case, where the ratio for the experiment performed at IGISOL-4 with Th (April, 2014) was calculated from six different values. This specific case can be considered an extreme one, most of the times one, or at most two, measurements were taking place for the same pair. In Fig. 4.4 each of these values is divided by the final result, as shown in Tab. 4.2. It should be further investigated if the observed deviation of the results can be attributed to systematic effects or not. On the other hand, the fact that three out of six results agree within uncertainties with the weighted mean can be considered satisfactory. It should be mentioned though that in all other cases where more than one measurements were available, the results were in satisfactory agreement to each other

4.2.3 Mass 97 Two different isomeric yield ratios could be extracted from this mass chain, 97Y and 97Nb.

97Y The isomeric pair of Y was measured with both targets by means of ion counting, and in addition with U target by employing γ-spectroscopy. Regarding the agreement of the results, the situation is more complicated. The results from the Th target disagree with each other. In the case of the U target, measured with both the Penning Trap and γ-spectroscopy, the ratios agree within uncertainties. It has to be noted though, that the latter has the biggest uncertainty of all measurements performed with this method (∼28%). Moreover, one result with Th target - the one performed at IGISOL-3 - agrees within uncertainties with the U case. It should also be mentioned that the result with the Thorium target from 2014 is much higher compared to the other ratios, for unknown

48 1.4

1.2

0.8 Deviation from the weighted mean

0.6 0 1 2 3 4 5 6 Number of experimental run

Fig. 4.4. In some cases the obtained isomeric yield ratio is calculated from the weighted mean of several values. In the ﬁgure the ratio of each such value is divided by the calculated arithmetic mean, for the case of 96Y, measured with Th target in April 2014. The black line represents the weighted mean, and the dashed red lines represent the uncertainties of this value.

reasons. The results from this work are in good agreement with Tanikawa’s ratios in all but one case (Th-2014).

97Nb For Nb only the U target was used. To deduce the yield ratio both the Penning Trap and γ-spectroscopy were employed. The results for these two measurements are in good agreement.

4.2.4 Mass 128 For this mass the isomeric yield ratio of 128Sn was extracted. It was measured by utilising the Penning Trap in the experiment with natTh target and using γ-spectroscopy with natU target. The results from the two different targets agree within errors. Nevertheless, the comparison between isomeric yield ratios from different ﬁssioning system should be done cautiously, as explained earlier, due to the different decay paths in the de-excitation of the ﬁssion fragments. The ratio reported in Tanikawa’s work is in agreement within uncer-

49 tainties with the present work for the case of the Th target, while for the U case the agreement within uncertainties is on the verge.

4.2.5 Mass 130 The isomeric yield ratio of 130Sn was measured in all experiments that were performed at the upgraded facility (IGISOL-4), but not in the old one (IGISOL- 3). For the γ-spectroscopy data no corrections due to contributions from the precursors were applied since these are considered insignificant, taking into account the yield of the fission products as measured in [15]. The result from June 2013 has the largest uncertainty, but it should be discarded since the spectrum was distorted from impurities of non identified elements. The agreement of the ratios for the experiments performed with U target, with both methods, is excellent. The ratio for the Th target though is considerably lower than the aforementioned ones. The comparison of the extracted ratios from this work with data available in the literature shows an agreement between the result from Th target and Tanikawa’s ratio.

4.3 General remarks In Fig. 4.5 the correlation of the results depending on the target is depicted, in order to investigate a possible dependence on the fissioning system. In the cases where more than one measurement for one nuclide from the same target existed, the weighted mean was calculated. It can be noticed that the yield ratios deduced by using the Th target are higher compared to the ones performed with U target, especially for the light mass fragments. Although some indications on a dependence of the fissioning system can be observed, more systematic studies on the same isomeric pairs from various fissioning systems are required before any unambiguous conclusions can be drawn. In Fig. 4.6 the isomeric yield ratio as a function of the spin difference of the states is illustrated. The yield ratio is larger than or at least around one, whenever the spin of the isomer is higher than that of the ground state. Specif- ically, in 81Ge and 97Nb, the ground state has higher spin than the isomer, and the obtained ratios are ∼0.3 and ∼0.08. In all other cases the ratio is larger than one, whenever the spin of the isomer is higher, with the only exception for nucleus 130Sn, whose ratio is equal or lower than one, depending on the experimental case. It should be highlighted that all the available data in the literature are based on γ-spectroscopy measurements, thus the quality of these studies partly depends on the accuracy of the available nuclear data, such as the γ-ray branching ratios. For the deduction of the yield a number of parameters, like the detector efficiency and the feeding to the nuclide of interest due to the β-decay of the precursors, should be taken into account. Each of these parameters

50 2

IYR(Th/U) 1.5 81Ge 96Y

97Y 1

130Sn 0.5

0 0 1 2 3 4 5

Fig. 4.5. Investigation of the dependence of the isomeric yield ratio on the ﬁssioning system. The dashed line shows the same isomeric yield ratio in both systems. On the y-axis the fraction of the isomeric yield ratio measured in the system of nat Th(p,f) over the system of nat U(p,f) is shown. contribute to the total uncertainty of the ratio, usually resulting in high uncertainties. The signiﬁcance of the method applied in this work by utilising the Penning Trap can be noticed in cases like 97Y. In all measurements performed by means of γ-spectroscopy the statistical uncertainties are rather high while with the IGISOL technique, they are noticeably reduced.

51 IYR vs Spin difference Uranium IYR 3 Y-97 Thorium U-(γ)

Y-96

1 Ge-81 Nb-97 Sn-128 Sn-130 0 −4 −2 0 2 4 6 8 Jm-Jgs

Fig. 4.6. In the ﬁgure the isomeric yield ratio as a function of the spin difference of the states is shown. It can be noticed that most of the times, when Jm-Jgs>0, the isomeric yield ratio exceeds one.

52 5. Summary and Conclusions

5.1 Summary In this work the yield ratios of six isomeric pairs were determined experimentally for 25 MeV proton-induced fission on natU and natTh. The measurements were performed at the Ion Guide Isotope Separator On-Line (IGISOL) facility at the University of Jyväskylä in several experimental campaigns, both at the old (IGISOL-3) and at the recently upgraded facility (IGISOL-4). Isomeric yield ratios of fission products (81Ge, 96Y, 97Y, 97Nb, 128Sn and 130Sn) with suitable half-lives were measured in a wide mass range. For the natU(p,f) system, there were three isomeric pairs measured for the first time (81Ge, 96Y and 97Nb), while there are no available data in the literature for all isomeric pairs measured in this study for the Th(p,f) system. For the measurements of the short-lived fission products the IGISOL method was employed and by employing the high resolving power of the Penning trap JYFLTRAP, isomeric states down to a few hundreds keV from the ground state could be resolved. A direct measurement of the isomeric fission yield ratios by means of ion counting in less than a second after their production was accomplished for the first time. γ-spectroscopy was also employed in the experiment of June 2013 in order to measure the product yields of the fission of natU and verify the consistency of the experimental method. The obtained isomeric yield ratios were also compared to data available in the literature, which are very scarce for the isomeric pairs measured specifically in the present work.

5.2 Conclusions An agreement within uncertainties of the obtained isomeric yields ratio could be observed in most cases, especially for the products of the same fissioning system. Nevertheless, a discrepancy was noticed in cases where a different actinide target was used, indicating a dependence of the produced isomeric yields on the fissioning system. As can be seen in Fig. 4.5 of section 4.3, the experimentally determined isomeric ratios produced by natTh are higher than the ones produced by natU, at least for the light products. On the other hand, the situation seems to be reversed for the heavy products. Since the data in this work are limited, more systematic studies on the same isomeric pairs from various fissioning systems are required before any unambiguous conclusions can be drawn.

53 In Fig. 4.6 of section 4.3, a correlation can be observed between the yield ratios and the spin difference of the measured states. Specifically, whenever the spin difference Jm − Jgs >0, the ratio is equal to or exceeds unity, while it becomes small when the spin difference is negative. Considering the general preference of the fragments to electromagnetically decay to the states with the minimum possible spin change ∆J, the tendency mentioned above could imply a hint for the spin of the produced fragments. As mentioned in section 1.3, the experimental determination of the isomeric yield ratios is one of the possible methods to deduce the angular momentum of the fission fragments. An advantage of the IGISOL-JYFLTRAP technique can be noticed in the case of 97Y, as the results from the Penning Trap show significantly lower uncertainties, compared to the ones from the γ-spectroscopy. By measuring the relative intensities of the isomeric states by means of γ-spectroscopy the accuracy of the results depend on a series of factors, such as the precision of the available nuclear data, resulting usually in high uncertainties. The new method applied here can contribute to lower relative uncertainties, since it is performed by means of ion counting. As mentioned earlier, the available data in the literature, especially for the case of proton-induced fission, are very rare. This work is part of a series of measurements planned to be performed at IGISOL to measure the relative intensities of various isomeric states with sufficiently long half-lifes and production rates at measurable levels. Thus, some more data will eventually be added to the presented here ones. Moreover, neutron-induced fission is planned to be implemented at IGISOL, since the independent yield of neutron-rich nuclides produced in fission is higher if this is induced by neutrons [26],[29]. Thus, it would be possible to observe the differences in the relative intensities of metastable states produced by neutron- and proton-induced fission for the same isomeric pairs.

54 Acknowledgements

I would like to acknowledge a lot of people for their help and support during these years. First of all, I would like to thank my supervisors for their feed- back and help in the accomplishment of this thesis. Their guidance was much appreciated and extremely valuable! To Mattias Lantz, for being always sup- portive, enthusiastic and easy going. His attitude that no work is wasted and that we can always learn something is a priceless lesson itself! To Andreas Solders, for his help, advices and new suggestions during every stage of this work and for his willingness to answer my questions any time, no matter how busy he was. His comments, always to the point were most welcome, even if I was caught by surprise sometimes! To Stephan Pomp, for sharing his deep knowledge and experience in nuclear physics and particularly in fission. Even the shortest discussion or the smallest comment could help me to put things in the right perspective. To Ali Al-Adili, whose comments always made me thinking one step further! His hard work and passion is a real example to follow. Very special thanks to Andrea Mattera, for being such a good colleague and friend. Or in a better order, a good friend and colleague... The time with him at the office, abroad and out of work activities is always a joy. I’m not sure how I could make it without his help in many different ways. Thanks once more for the good team work and the pleasant atmosphere you all create at "högkvarteret" through all these years. I’m very gratified to work in there. I would also like to thank Dmitry Gorelov, Heikki Penttilä and everyone from the IGISOL group for their help and hospitality every time we have been in Jyväskylä. To all people in the nuclear reactions group and TK for the nice environ- ment: to Alexander Prokofiev for his help, collaboration and sharing his experience in a series of neutron related experiments, to Diego for the interesting discussions in the late lunches, to Kaj for sharing the office with him in my first months in Sweden and introducing me to the Swedish life style, to Ce- cilia, Erik, Erwin, Henrik, Petter, Augusto, Michael and everyone else. To Kostas and Foteini for being such good friends and neighbours. To Alex, Vicky, Federico and Cristina for their true friendship and for sharing lately the same fears and anxiety as we do. Foremost, to Katerina who has been always standing by me through this journey from the beginning and for the best present she could ever make me six months ago, the little Elias-Sebastian who changed my life once and forever. Home has a different meaning when you are both there! "I wanna show you something", she said ...

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